A very common circuit problem in introductory physics
involves three lamps in a simple circuit. Students generally can predict
the behavior of the circuit when the three lamps are in parallel, but have
no clear understanding of their behavior when the same lamps are placed
in series. This apparatus allows the exploration of these circuit concepts.

Support required for apparatus:

Approximate size Base :1foot by 6 in, 2 feet tall

Does this apparatus require Electrical Power? yes

Will you be present to set up your apparatus? yes

Other support needed for the proper operation of this
apparatus: none

Three Lamps in Parallel and
Series

Abstract (same as abstract above)

A very common circuit problem in introductory physics
involves three lamps in a simple circuit[1]. Students generally can predict
the behavior of the circuit when the three lamps are in parallel, but have
no clear understanding of their behavior when the same lamps are placed
in series. This apparatus incorporates three everyday light bulbs on lamp
sockets and a series of knife switches which can allow setting these bulbs
up in either series or parallel. This apparatus is used as a conclusion
to simple resistance circuit theory before entering branching circuits.

Theory

Three lamps in a simple circuit can be treated as
three fixed resistors in the circuit and a simple solution can be determined
using established addition of resistors in series and parallel. Figure
1 shows a circuit that includes knife switches that allow configuration
of the three lamps into both parallel and series circuits.

Figure 1. Three lamps in the circuit(L1,
L2, L3) can be configured to be in parallel and series
using the switches (S1, S2, S3).

The circuit shows an AC source. Even if AC theory
has not been covered, the following description is accurate by using the
rms voltage in the calculation, thereby suppressing the AC nature of the
circuit. The switch S0 is a safety cutoff if the apparatus cover
is opened and does not play a part in the physics of the circuit. The three
lamps L1, L2, and L3 will be treated as
three resistors R1, R2 and R3.

When the three switches are all switched to the outside,
the circuit is completely parallel. In this situation the voltage across
all three lamps is the line voltage. All three lamps show normal brightness.
For this demonstration L1 = 60 W, L2 = 40 W and L3
= 25 W were used. Combining Watt’s law and Ohm’s law will allow the determination
of the resistance and current of each lamp. A summary of the equations
for voltage, current, resistance and power is given in Table 1. The numerical
values are not very accurate due to the change in resistance when a lamps
heat, and are not included.

Table 1. Summary of calculations for the circuit
in Figure 1, in both the Parallel and Series configurations.

Element

Voltage

Current

Resistance

Power

Parallel

L1

V

V/R1

R1=V2/P1

P1

L2

V

V/R2

R2=V2/P2

P2

L3

V

V/R3

R3=V2/P3

P3

Series

L1

I*R1

V/(Rtot)

R1

I2*R1

L2

I*R2

V/(Rtot)

R2

I2*R2

L3

I*R3

V/(Rtot)

R3

I2*R3

When the three switches are all switched to the inside,
the circuit is completely series. At this point all the three lamps must
have the same current. The voltage is "shared" among the lamps
to make the total voltage drop add up to the line voltage. Ignoring the
temperature dependence of the resistance of each lamp, a simple application
of Watt’s and Ohm’s laws will show that the lamp with the lowest wattage
rating will receive the largest portion of the voltage, and therefore will
be brightest. A summary of the equations for voltage, current, resistance
and power is given in Table 1. For the wattage listed above, L1
will get 20.4% of the voltage, L2 will get 30.6% and L3
will get 49%. These ratios will vary for different wattage lamps but are
not dependent on the line voltage. The voltage in L1 is not
high enough to make it light. This tends to be counterintuitive for most
students, but is easily calculated and demonstrated.

Materials list

The materials needed for construction are listed
in Table 2.

Table 2. Materials needed including costs.

Item

Amount

Description

Cost

1

1

12"x 24" x ½"
piece of wood

2.94

2

3

Flush mount light bases

7.38

3

1

Extension Cord

0.97

4

3

SPDT knife switches

7.17

5

1

Terminal connector

1.00

6

2

Hinges

4.26

7

pkg

Terminal lugs

1.40

8

3 ft

Black and Red wire

5.00

9

3 ft

Aluminum angle iron

3.35

5 ft2

Thin Plexiglas

7.11

misc

Hardware

2.00

1

Kill Switch

3.94

Total Cost

$46.52

All materials are available at mega-hardware stores
such as Lowe’s or Home Depot except items number 4 & 5. Item 4 is available
from Central Scientific Company and 5 from Newark Electronics. Nothing
on the list is critical and substitutions can be easily made. The author
suggests that the knife switches and visible wiring and terminals be used
to allow complete visualization of the circuit.

Construction and Set-up

The constructed apparatus is shown in Figure 2. In
the figure the knife switches are set to form the Series circuit. The 25
W is the brightest, the 40 Watt is very dim and the 60 W does not seem
to be lit. If the knife switches were reversed, the circuit would be in
Parallel, and the lamps would show their normal brightness, with the 60
W being the brightest and the 25 W being the dimmest.

Figure 2. Apparatus for three lamps set in Series.

The construction is open, as long the circuit diagram
in Figure 1 is followed. It was attempted to key the wire colors to maximize
the difference between the series and parallel circuit, but this was not
very successful, due to the dual use of some wires and single use of others.
As stated above, the wire connections and knife switches are exposed to
allow viewing of the various current paths available to the circuit. For
safety, a high current kill switch is mounted in one of the cover hinges.
The main AC power runs through this switch. If the lid is raised the power
is cut off. Due to the simplicity of the circuit, this apparatus is not
sensitive to current surges or miss-set knife switches.

Execution

We generally complete the parallel calculation in
class before using the apparatus. After the currents and voltages are determined,
the students are requested to set the system up in the parallel configuration,
and to show that everything goes as expected. Next the students are requested
to predict the behavior of the circuit in series. They set up the circuit
and test to see the outcome. Many students predict behavior inconsistent
with actual performance. After a simple circuit analysis, the actual performance
is easily understood.

Conclusions

This apparatus is useful in concluding the concepts
of simple parallel and series circuit analysis. Its simplicity and use
of everyday components seem to be appreciated by students. The actual wattage
used by the lamps in the series configuration are numerically different
from the calculations due to the variance of resistance with temperature
in a normal incandescent lamp, but the qualitative nature is very illustrative.
Additionally, discussions about the temperature dependence can be used
to compare and contrast the idealization of theory and the real behavior
of circuit elements. Other lamp combinations are possible, but 60:40:25
seems to allow the clearest delineation of brightness in the series mode.